Extended Bose–Hubbard model with dipolar excitons

The Hubbard model constitutes one of the most celebrated theoretical frameworks of condensed-matter physics. It describes strongly correlated phases of interacting quantum particles confined in lattice potentials^1,2. For bosons, the Hubbard Hamiltonian has been deeply scrutinized for short-range on-site interactions^3–6. However, accessing longer-range couplings has remained elusive experimentally⁷. This marks the frontier towards the extended Bose–Hubbard Hamiltonian, which enables insulating ordered phases at fractional lattice fillings^8–12. Here we implement this Hamiltonian by confining semiconductor dipolar excitons in an artificial two-dimensional square lattice. Strong dipolar repulsions between nearest-neighbour lattice sites then stabilize an insulating state at half filling. This characteristic feature of the extended Bose–Hubbard model exhibits the signatures theoretically expected for a chequerboard spatial order. Our work thus highlights that dipolar excitons enable controlled implementations of boson-like arrays with strong off-site interactions, in lattices with programmable geometries and more than 100 sites.